Answer :
To solve the inequality [tex]\(38.4 > \frac{x}{-3.3}\)[/tex], follow these steps:
1. Understand the Inequality: We need to isolate [tex]\(x\)[/tex] on one side. Currently, [tex]\(x\)[/tex] is divided by [tex]\(-3.3\)[/tex].
2. Multiply Both Sides by [tex]\(-3.3\)[/tex]: To eliminate the division, multiply both sides of the inequality by [tex]\(-3.3\)[/tex]. Remember, whenever you multiply or divide by a negative number in an inequality, the inequality sign flips.
[tex]\[
38.4 \times (-3.3) < x
\][/tex]
3. Calculate the Multiplication: Perform the multiplication:
[tex]\[
38.4 \times (-3.3) = -126.72
\][/tex]
So, the inequality becomes:
[tex]\[
-126.72 < x
\][/tex]
4. Solution: The solution is [tex]\(x > -126.72\)[/tex]. This tells us that [tex]\(x\)[/tex] can be any number greater than [tex]\(-126.72\)[/tex].
5. Graphing the Solution:
- On a number line, draw an open circle at [tex]\(-126.72\)[/tex] to indicate that [tex]\(-126.72\)[/tex] is not included in the solution.
- Shade or draw an arrow to the right of [tex]\(-126.72\)[/tex] to represent all numbers greater than [tex]\(-126.72\)[/tex].
This visual indicates that any number to the right of [tex]\(-126.72\)[/tex] fulfills the condition [tex]\(x > -126.72\)[/tex].
1. Understand the Inequality: We need to isolate [tex]\(x\)[/tex] on one side. Currently, [tex]\(x\)[/tex] is divided by [tex]\(-3.3\)[/tex].
2. Multiply Both Sides by [tex]\(-3.3\)[/tex]: To eliminate the division, multiply both sides of the inequality by [tex]\(-3.3\)[/tex]. Remember, whenever you multiply or divide by a negative number in an inequality, the inequality sign flips.
[tex]\[
38.4 \times (-3.3) < x
\][/tex]
3. Calculate the Multiplication: Perform the multiplication:
[tex]\[
38.4 \times (-3.3) = -126.72
\][/tex]
So, the inequality becomes:
[tex]\[
-126.72 < x
\][/tex]
4. Solution: The solution is [tex]\(x > -126.72\)[/tex]. This tells us that [tex]\(x\)[/tex] can be any number greater than [tex]\(-126.72\)[/tex].
5. Graphing the Solution:
- On a number line, draw an open circle at [tex]\(-126.72\)[/tex] to indicate that [tex]\(-126.72\)[/tex] is not included in the solution.
- Shade or draw an arrow to the right of [tex]\(-126.72\)[/tex] to represent all numbers greater than [tex]\(-126.72\)[/tex].
This visual indicates that any number to the right of [tex]\(-126.72\)[/tex] fulfills the condition [tex]\(x > -126.72\)[/tex].
